Towards wave extraction in numerical relativity: the quasi-Kinnersley frame

TL;DR

This paper introduces the quasi-Kinnersley frame, a method for extracting physically meaningful gravitational radiation information in numerical relativity, applicable even in strongly non-perturbative black hole spacetimes.

Contribution

The paper proposes a new approach to identify an adapted null tetrad, called the quasi-Kinnersley frame, directly from the numerical metric without prior background knowledge.

Findings

Explicit solution for tetrad transformation to find the quasi-Kinnersley frame.

Applicable to strongly non-perturbative spacetime scenarios.

Enables invariant gravitational wave extraction in numerical relativity.

Abstract

The Newman-Penrose formalism may be used in numerical relativity to extract coordinate-invariant information about gravitational radiation emitted in strong-field dynamical scenarios. The main challenge in doing so is to identify a null tetrad appropriately adapted to the simulated geometry such that Newman-Penrose quantities computed relative to it have an invariant physical meaning. In black hole perturbation theory, the Teukolsky formalism uses such adapted tetrads, those which differ only perturbatively from the background Kinnersley tetrad. At late times, numerical simulations of astrophysical processes producing isolated black holes ought to admit descriptions in the Teukolsky formalism. However, adapted tetrads in this context must be identified using only the numerically computed metric, since no background Kerr geometry is known a priori. To do this, this paper introduces the notion of a quasi-Kinnersley frame. This frame, when space-time is perturbatively close to Kerr, approximates the background Kinnersley frame. However, it remains calculable much more generally, in space-times non-perturbatively different from Kerr. We give an explicit solution for the tetrad transformation which is required in order to find this frame in a general space-time.